Thank you Ant_222 very much , but maybe my poor expression in English has led to your not understanding exactly what I mean .When I say "I
could /might have loved him from that moment " I mean "
Perhaps I have loved him since then"(I'm not sure thether I have loved him or not ). If you just say " I have loved him since then" without " perhaps " , it would mean I 'm sure I started loving him right at the moment we first met.
Hopefully , you will understand what I really mean, and will help me say in a correct and natural way.
Best wishes